# 2D point light shadow - depth interpolation problem

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I render the depth-values of the right Frustum of the light into a texture which is 1024x1 pixels in size.

I project the vertices myself, so I dont use the w coordinate.

This is my projection into the shadow-map. "vs.lightSpace" means that all vertices are in the coordinate-system of the light. (0,0) is it's origin.

	gl_Position = vec4(
vs.lightSpace.y / vs.lightSpace.x,
0.0f,
depthToHom(vs.lightSpace.x),
1.0f);

float depthToHom(float depth) {
float near = 0.5f;
float far  = 10.0f;
return depth * 2.0f / (far - near) + (-far - near) / (far - near);
}


As you can see the depth-values are not interpolated correctly. On long edges there is a round curve in the shadow. Is this because I don't divide correctly? The big white circle is supposed to be a point-light.

To sample the depth I use:

float depth = texture(shadowMap, vec2((lightSpace.y / lightSpace.x + 1.0f) * 0.5f, 0.5f)).x;

if(depthToNorm(lightSpace.x) > depth)
{
//... ... ...
}

float depthToNorm(float depth) {
float near = 0.5f;
float far  = 10.0f;
return depth * (1.0f / (far - near)) + (-near) / (far - near);
}

Edited by stefthedrummer

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I once optimized 2d point light system and I noticed that easiest and fastest way to do it for many point light was to render all blockers to big single channel fbo. Then I calculated all shadow maps at once to (point lights x shadow map width) size fbo using screenspace raytracing. At that point drawing lights was really fast and shadow test was single texture lookup. Scene was always rendered just two times no matter how many lights was in scene. This way I could easily do 8k shadowed point lights in realtime(>60fps).(My laptop max texture width)

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...using screenspace raytracing.

What do you mean by "screenspace raytracing".

Do you mean:

for every light L - and every angle Alpha - you start at the origin of L and trace the direction given by Alpha until you hit a blocker in your fbo?

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I still want to known, where my math is wrong. Every context in my rendering is linear. So why do I see a curve?!

When I insert more points it gets better.

I dumped the content of my shadow-map to see whats wrong.

(The two color-transitions represent the content of the shadowMap - you can see - they are not the same - even though they should be)

Edited by stefthedrummer

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I fixed the problem.

The thing is that you can't do:

gl_Position = vec4(
vs.lightSpace.y / vs.lightSpace.x,
0.0f,
depthToHom(vs.lightSpace.x),
1.0f);


because the

vs.lightSpace.y / vs.lightSpace.x


is a perspective divide - and you can't interpolate already divided values.

The Fix:

gl_Position = vec4(
vs.lightSpace.y,
... ... ...,
... ... ...,
vs.lightSpace.x);


The divident and divisor of the perspective projection have to be interpolated independently in order to guarantee a perspective correct interpolation of depth values.

also the "... ... ..." have to be modified, but that's not essential to the point I'm trying to make.

- This cost me a hole day to figure out-

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